Geometric Frustration and Solid-Solid Transitions in Model 2D Tissue

Physical Review Letters
Michael MosheM Cristina Marchetti

Abstract

We study the mechanical behavior of two-dimensional cellular tissues by formulating the continuum limit of discrete vertex models based on an energy that penalizes departures from a target area A_{0} and a target perimeter P_{0} for the component cells of the tissue. As the dimensionless target shape index s_{0}=(P_{0}/sqrt[A_{0}]) is varied, we find a transition from a soft elastic regime for a compatible target perimeter and area to a stiffer nonlinear elastic regime frustrated by geometric incompatibility. We show that the ground state in the soft regime has a family of degenerate solutions associated with zero modes for the target area and perimeter. The onset of geometric incompatibility at a critical s_{0}^{c} lifts this degeneracy. The resultant energy gap leads to a nonlinear elastic response distinct from that obtained in classical elasticity models. We draw an analogy between cellular tissues and anelastic deformations in solids.

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Nov 26, 2019·Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences·N Gorbushin, L Truskinovsky
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May 20, 2021·Physical Review. E·N Gorbushin, L Truskinovsky
Aug 31, 2021·Current Opinion in Cell Biology·Elizabeth Lawson-Keister, M Lisa Manning

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